ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

3. METHODS
3.1. Bones
The shoulder model is based on the anatomical dataset of a male human [15][16]. We assumed a
bodyweight (BW) of 75 kg. It includes the thorax, clavicula, scapula, humerus and the linking joints
sternoclavicular, acromioclavicular and glenohumeral joint (fig. 1). The bones are modelled as rigid
bodies. They are represented by the bones reference coordinate system [17] and the insertion points
of the muscles attached to that bone [16]. The thorax is fixed in global coordinates. It is represented
by an ellipsoid. The scapula is attached to that ellipsoid and can glide along its surface. The sternoclavicular
and acromioclavicular joint are modelled as spherical joints. The remaining rotational degrees
of freedom are restricted by boundary conditions. The glenohumeral joint is modelled as
spherical joint during positioning steps, but translational degrees of freedom are liberated during
loading. The arm weight is 3.75 kg (5% BW).
3.2. Cartilage
A cartilage layer is reconstructed within the glenoid cavity. A Neo Hookean material is chosen [18].
The Neo-Hookean potential is defined as follows :
w=c ˙
0(
I 1−3)
where c0 is the material constant:
c0=1.8 J
m 3
and I 1 the first invariant of the right Cauchy–Green stress tensor:
2 2 2
I 1 =λ 1+λ2+λ3
with the prinicpal strains λi . The cartilage is meshed using 1300 hexaedral quadratic elements
(fig. 2). They are linked to the rigid scapula on the medial side. The articular contact with the humeral
head is defined to be frictionless.
Fig. 1.: The model of the upper limb
including bones and wrapped muscles.
Fig. 2.: Scapula with meshed glenoid
cavity.